# gentzen

## The Proof Widget

Logical System

2013

Some predicate logic proofs or derivations using Gentzen calculus. Try to prove them. Click on a line to select it. Select one or more lines, apply the appropriate rule off the Rules menu. (Click 'Derive It' off the Wizard Menu, if you want help).

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Logical System

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## Tutorial 25 ...

Logical System
###### 12/26/13

You now have the tools to appraise arguments to the level of detail offered by predicate logic.

Let us run through how these might be used with a long and difficult example.

Consider the argument

## Tutorial 24: The restrictions on the quantificational rules

Topic
Logical System

### Skill to be acquired:

To understand the concepts of scope, free, bound, and free for.

### Why this is useful:

The new predicate rules of inference using quantifiers have restrictions on them which are expressed in terms of these concepts.

## Tutorial 23: The semantics of relations

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Logical System

### The Tutorial

The semantics of relations proceeds in much the way one would expect-- the new item that has to be taken account of is the order of the terms (because, for example, Tab is not at all the same thing as Tba -- Arthur being taller than Beryl is not the same as Beryl being taller than Arthur).

Let us start with an Interpretation

Interpretation 1

Universe= {a,b}
F={a}